How to make the 3d manipulator act parallel to a plane
Select (a face in) the plane
Create a Custom Orientation (CtrlAltSpace)
(Check 'Use after creation' and possibly 'Overwrite previous' in the tool region,if you don't want to bother to name the orientation, and/or don't need it later)
Any translation you now make with G-ShiftZ-ShiftZ will be parallel to the plane you selected.